Interpretation of NIMS and SSI Images on the Jovian Cloud Structure

Transcription

1 Icarus 150, (2001) doi: /icar , avaiabe onine at on Interpretation of NIMS and SSI Images on the Jovian Coud Structure U. A. Dyudina, A. P. Ingerso, and G. E. Danieson , Geoogica and Panetary Sciences, Catech, Pasadena, Caifornia E-mai: K. H. Baines and R. W. Carson Jet Propusion Laboratory, Pasadena, Caifornia and The Gaieo NIMS and SSI Teams Received February 23, 1999; revised November 13, 2000 We present maps of jovian coud properties derived from images taken simutaneousy by the Gaieo soid state imaging system (SSI) and the near-infrared mapping spectrometer (NIMS) at 26 visibe and near-infrared waveengths, ranging from 0.41 to 5.2 µm. Three regions the Great Red Spot (GRS), a 5-micron Hot Spot, and one of the White Ovas were studied. We perform a principa component anaysis (PCA) on the mutispectra images. The principa components (PCs), aso known as empirica orthogona functions, depend ony on waveength. The first PC is that spectra function which, when mutipied by an optimay chosen number (ampitude factor) at each pixe ocation and subtracted from the spectrum there, minimizes the variance for the image as a whoe. Succeeding PCs minimize the residua variance after the earier PCs have been subtracted off. We find that the pixe-to-pixe variations at the different waveengths are highy correated, such that the first three PCs expain 91% of the variance in the spectra. Further, one can estimate the ampitudes of the first two PCs using ony the four SSI waveengths and sti expain 62% of the variance of the entire spectrum. This can be an advantage when trying to cassify features that are resoved in the SSI images but not in the NIMS images. The first PC in a three regions shows negative correation between 5 µm emission and refected soar ight in both atmospheric windows and the methane and ammonia absorption bands. Thus most of the bright, opticay thick couds bocking therma emission are aso extended verticay to the upper troposphere. The first PC at the GRS shows a negative correation between the vioet and a other bands except 5 µm, for which the correation is positive. Thus in the GRS there is a red chromophore (absorbing in the vioet, refecting at onger waveengths) which is associated with couds that bock 5-µm emission. There is no such correation at the hot spot and white ova regions and therefore no chromophore associated with couds. The second PC shows a positive correation between the depth of the methane and ammonia absorption bands and brightness at other visibe and near-ir waveengths; there is aso a negative correation between these quantities and 5-µm emission. Thus some of the bright, opticay thick couds bocking therma emission are deep and do not extend verticay to the upper troposphere. A coor image composed using the first three PCs shows areas of unusua spectra, which appear in distinct coors. An exampe is the sma convective stormike coud to the northwest of the GRS. This coud is highy refective at ong waveengths (4 µm) and might indicate unusuay arge partices. c 2001 Academic Press Key Words: atmospheric structure; jovian atmosphere; image processing. 1. INTRODUCTION One of the principa goas of the Gaieo mission to Jupiter is to determine how the couds are distributed in the jovian atmosphere. Knowedge of the coud distribution is crucia for understanding atmospheric composition and motion and other processes on Jupiter. Studying couds is especiay important as they are the primary source of information about the dynamics of the jovian atmosphere. The pre-gaieo view of the couds was based on ground-based spectra studies, poarization properties of the atmosphere (detected by the Pioneer spacecrafts), Voyager visibe imaging, the Voyager infrared IRIS experiment, and other remote sensing techniques. A detaied review of these studies and the coud structure derived from these observations can be found in West et a. (1986); see aso Sada et a. (1996), Satoh and Kawabata (1994), and Beebe (1997). The Gaieo mission brings new constraints to the coud modes. Both Gaieo probe in situ data (Niemann et a. 1996) and Gaieo orbiter observations (Carson et a. 1996, Beton et a. 1996) have fueed recent deveopment of new coud and dynamica modes (Banfied et a. 1998, Weir et a. 1997, Baines et a. 1999, Orton et a. 1998, Irwin et a. 1998). We use Gaieo soid state imaging (SSI) (Vasavada et a. 1998) and near-infrared mapping spectrometer (NIMS) data (Weir et a. 1997, Baines et a. 1999) to derive and map properties /01 $35.00 Copyright c 2001 by Academic Press A rights of reproduction in any form reserved.

2 220 DYUDINA ET AL. of the observed couds at the spatia resoution of the NIMS instrument ( km). We study the regions of the Great Red Spot (GRS), the region to the south of one of the Hot Spots, and one of the White Ovas. To separate and map the strongest variation in the spectra we perform principa component anaysis (PCA) on the image data. Using PCA we summarize 91% of the brightness variance from 26 spatia maps of the GRS (one map per each waveength) into one fase coor map. We make a quaitative comparison and interpretation of the spectra representing parts of the GRS using this map. We show that a reconstruction of the images at NIMS waveengths can be done using SSI images and PCA resuts. This study is important because it is the first to combine high spatia resoution (22 36 km/pixe of SSI and km/pixe of NIMS) with broad spectra coverage (26 waveengths from 0.41 to 5.2 µm). As a resut, high-resoution coud structure is derived. The use of PCA aows us to separate parts of the regions having different spectra, reduce the noise, and separate spatia and spectra variation in the data. We offer quaitative interpretations ony. Quantitative interpretations are beyond the scope of this paper. We did some preiminary experiments using a radiative transfer mode by West et a. (1986). Athough the mode resuts are in rough agreement with our quaitative interpretation, some of the parameter dependences in the mode are noninear. PCA is a inear east-squares anaysis. Therefore it is not possibe to find an exact quantitative fit to the inear PCA resuts. An additiona modeing compication is that before modeing spatia variations in the spectra one needs to mode the averaged spectrum. That is best done with a more compete spectrum, i.e., more waveengths. Such data do exist, particuary for NIMS (Irwin et a. 1998), but these data have imited spatia coverage. The three regions considered here are the ony regions where we have SSI and NIMS data with good spatia coverage. Accordingy, instead of modeing, we concentrate here on the spatia correations and quaitative comparison of the areas on Jupiter that are we resoved spatiay. The structure of this paper is as foows. In Section 2 we describe the observationa data. Section 3 describes principa component anaysis. Section 4 contains PCA resuts and interpretation of them in terms of coud structure. We anayze errors in Section 5. Section 6 contains the discussion of our resuts in terms of atmospheric motion. 2. THE DATA Two instruments on the Gaieo orbiter observed the Great Red Spot, the Hot Spot, and the White Ova, as we as their surroundings, in on orbits G1, E4, and E6 respectivey. The near-infrared mapping spectrometer mapped the areas in near-ir waveengths ranging from µm to µm. Simutaneousy with NIMS, the soid state imager mapped the two regions at four waveengths (0.410, 0.727, 0.756, and µm). For the GRS the time difference between NIMS and SSI images was approximatey 15 minutes (see Tabe I). TABLE I Data Characteristics Number of Spatia resoution NIMS SSI time waveengths (km/pixe) separation GRS NIMS minutes SSI Hot Spot NIMS hours SSI White Ova NIMS hours SSI During this short time the observed couds did not move more than one NIMS pixe. For the Hot Spot and the White Ova the time differences were 20 and 12 hours respectivey. Individua couds coud have moved by at most 1 2 NIMS pixes; therefore most features on NIMS and SSI images remain simiar. We combined NIMS and SSI data for each region. Then we studied how the combined 26-waveength spectrum changed from pixe to pixe. One NIMS waveength (2.435 µm) from the GRS data set was not considered because the image shows no significant signa, and therefore it is of potentia interest as an indicator of strong atmospheric absorption but is useess for our brightness distribution anaysis. The Hot Spot and White Ova images were anayzed at 26 waveengths corresponding to the GRS waveengths, such that the PCA resuts can be compared for the three data sets. The images of the GRS are shown in Fig. 1. Part of the Hot Spot image (Fig. 2) at NIMS waveengths was shadowed by sateite Europa. This area was removed from our data anaysis. Different scattering geometries of NIMS and SSI are important for the Hot Spot and White Ova data (Figs. 2 and 3). For the Hot Spot the phase ange is 16 for NIMS and 56 for SSI. For the White Ova the phase ange is 20 for NIMS and 48 for SSI. The White Ova images were taken cose to the terminator (with an incident ange of about 60 for both SSI and NIMS). As a resut, at the White Ova, high atmospheric haze obscured the ower couds in the waveengths of high gaseous absorption and there is no significant brightness variation in some of the NIMS images (see Fig. 3). Because of that effect and because of the coud motion due to the NIMS SSI time separation, the resuts for the Hot Spot and the White Ova are more uncertain than those for the GRS. However, taking into account the uniqueness of these simutaneous observations, the Hot Spot and White Ova data are interesting to compare with the GRS resuts. The effects of combining images having different spatia resoution, observationa noise effects, and waveength uncertainty are discussed in Sections 5.1, 5.2, and DATA ANALYSIS 3.1. Appication of PCA on the Image Data Athough PCA is a standard technique (Murtagh and Heck 1987), each appication is different. We summarize our approach beow.

3 JOVIAN CLOUD STRUCTURE FROM NIMS AND SSI IMAGES 221 FIG. 1. Combined SSI NIMS image set for the GRS. The abes to the right of the image indicate the device that took the image (NIMS or SSI), the waveength in µm, and the gas or soid having the absorption band at this waveength. Spectra resoution (bandwidth) is about µm for λ<1µm and µm for λ>1µm. Images at λ<4.5µm show the sunight refected from the couds and absorbed by the atmospheric gases above the couds. Images at λ>4.5µm show therma emission from the jovian interior.

4 222 DYUDINA ET AL. FIG. 2. Combined SSI NIMS image set for the hot spot. The circuar area on each image is the shadow of Europa. Consider repeated measurements (e.g., pixes) of some particuar properties (e.g., brightness at different waveengths) of a physica object. Ca the number of measurements n and number of properties m. Now we can think of our data set as n data points in m-dimensiona space. For the purpose of this work we consider each pixe on the 26 Gaieo images as one measurement of m = 26 properties brightnesses X p (λ) in 26 different waveengths λ, where the index p denotes pixe. In other words, each pixe is a data point in a 26-dimensiona waveength space. For convenience we index waveengths by such that = 1, 2,...,26 corresponds to λ = µm, µm,..., µm. Then X p corresponds to X p (λ). We do not pay specia attention to the mean spectrum (averaged over a pixes in the image), as our data have a more interesting aspect spatia variation at high resoution. The mean spectra for the GRS, Hot Spot, and White Ova regions are simiar (see Fig. 4). Some properties of the mean spectrum wi be discussed in Section 4.1. We subtract the mean spectrum from each data point to get the deviation from the mean: X p = X p 1 n pixes X p n. pixes p=1 To treat measurements in the different waveengths equay, deviations at each waveength are normaized by the standard deviation σ over the image at this waveength. We wi ca this

5 JOVIAN CLOUD STRUCTURE FROM NIMS AND SSI IMAGES 223 FIG. 3. Combined SSI NIMS image set for the White Ova. method standard normaization: δx p = X p where (σ ) 2 = 1 σ n pixes n pixes p=1 ( p) 2. X Another, noise-based normaization wi be discussed in Section 5.3. PCA seeks the best approximation of the data set by a few inear functions (PCs) of m waveengths. The ith principa component can be written as a vector u i (or PC i), where = 1, 2,...,m. The vectors are orthogona and normaized, so that m =1 u i u j = δ i, j for any i, j, where δ i, j = 1 ifi = j, δ i,j = 0 ifi j. Mutipying the first few principa components by the corresponding ampitudes A p i at the pixe p and summing, we can approximate the observed deviation from the mean at this pixe as δx p = q i=1 A p i ui + ( R p ) q, where (R p ) q is a residua brightness in point p at the th waveength after approximation by the first q PCs. Note that u i is defined for the image as a whoe, whereas the ampitude A p i is different for each pixe. The approximation is evauated by minimizing the sum of the squares of the residuas n pixes m (( p) 2. R q) p=1 =1

6 224 DYUDINA ET AL. FIG. 4. The mean spectra for the GRS, Hot Spot, and White Ova regions. The combined 26-waveength spectrum is normaized by the incident soar ight (I/F). To combine NIMS and SSI spectra, we renormaized the NIMS part of the spectrum such that I/F at µm (NIMS) coincided with I/F at µm (SSI). At λ>4.5µm therma emission from Jupiter is stronger than the refected ight (I/F > 1). Principa components can be understood as a set of basis vectors in m-dimensiona space chosen so that the maximum pixe-to-pixe variation in the data beongs to the subspace formed by one, two, three, etc. basis vectors. The probem can be soved as an eigenvaue probem for the correation matrix S of m deviations averaged over a image pixes (see the derivation in Murtagh and Heck (1987), chapter 2.2.3): Su = αu, where S 1 2 = n pixes p=1 ( δx p 1 δx p 2 ). It can be shown that the eigenvaue α gives the fraction of the tota variance projected on the m-dimensiona vector u (standard deviation aong this axis). The m soutions ordered in decreasing order of α s are the principa components. In terms of the new coordinate system, the ampitude A p i is a coordinate of the pth data point in the ith dimension the projection of the data vector δx p onto the new unit vector u i. Ampitudes A p i form a map of scaar coefficients according to the image pixes p for each ith principa component u i Limitations of the Method PCA gives usefu resuts ony in the case of high correation (as in our data when the first eigenvaues are much arger than the next ones). In this case data can be meaningfuy reduced to a few dimensions. PCA is a purey empirica method, and additiona anaysis is needed to expain the physics of the observed object. 4. RESULTS 4.1. PCA Resuts Using PCA we found that the pixe-to-pixe variations of brightness in the different waveengths are highy correated. This high correation suggests that ony a few independent spectra functions (PCs) are needed to describe most of the brightness variation. Namey, PCA for the GRS shows that 63% of the tota variance is produced by the first principa component aone, 23% by the second one, and 4% by the third one. For the Hot Spot region, the corresponding percentages are 45% (PC 1 ), 17% (PC 2 ), and 6% (PC 3 ). For the White Ova the percentages are 61% (PC 1 ), 12% (PC 2 ), and 5% (PC 3 ). The ower percentages for the Hot Spot and White Ova regions are ikey due to the data being noisier (see Figs. 1, 2, and 3) and therefore a arger fraction of the variance is an uncorreated noise. Before describing the principa components we describe some quaitative features of the spectra (Fig. 5b). First, high refectance (I/F) occurs in the atmospheric windows (insets I IV in Fig. 5b), where the absorption of the atmospheric gases above the couds is minima. If the area is brighter than its surroundings in the atmospheric window, it indicates a coud that is opticay thicker than its surroundings at this waveength. Waveengths of ow refectance are gaseous absorption bands (insets V VII in Fig. 5b). A considerabe fraction of the soar ight is absorbed above the couds at these waveengths. If two couds differ in brightness in absorption bands but are equay bright in an atmospheric window, it means the darker coud is ocated deeper in the atmosphere. Equivaenty, the darker coud has fewer scatterers at high atitude (ess haze). However, the effects of partice size, singe scattering abedo, coud opacity, and coud eevation are hard to distinguish with our data. As PCA shows, the data have ony a few independent modes of variation. Accordingy we choose coud eevation and opacity to interpret the data, treating these parameters as the most important ones for the refected spectrum. Figure 6 shows the first four principa components (PC 1,PC 2, PC 3, and PC 4 ) for the GRS, Hot Spot, and White Ova regions. The refected sunight described by PC 1 (positive PC 1 vaues at λ<4.5µm) is anticorreated with 5-µm therma emission (negative PC 1 vaues at λ>4.5µm). The vaues of neary zero correation mean ow signa-to-noise ratio in the images at strong absorption bands, as can be seen in Figs. 1, 2, and 3. The ampitude maps for PC 1 are shown in Fig. 7. The ight areas show positive coefficients for PC 1. These are areas of high refection and ow 5-µm emission. Dark areas show ow refection and high 5-µm emission. The fact that refected ight is anticorreated with therma emission was extensivey noted in previous studies (see West et a. 1986, Beebe 1997) by simpe comparison of the images taken in waveengths shortward of 4.5 µm and in 5 µm. That gave rise to the idea that in some areas we see couds refecting sunight and bocking 5-µm emission from the jovian interior. In other ess coudy areas, sunight gets absorbed deep in the atmosphere and therma emission escapes to space (see summaries in Beebe (1997) and West et a. (1986)). According to this interpretation, the coefficient in front of PC 1 is a measure of coudiness. Light areas on the PC 1 map are coudier than the dark ones. Since PC 1 is positive both inside and outside of the absorption bands, the couds cannot be confined to ow atitudes. The coud tops must be high.

7 JOVIAN CLOUD STRUCTURE FROM NIMS AND SSI IMAGES 225 FIG. 5. (a) Fase coor map of GRS composed from the maps of PC 1,PC 2, and PC 3 as red, green, and bue, respectivey. Areas shown in the same coor have simiar spectra. (b) Spectra for the different parts of the GRS. Each spectrum (a, b, c, d) is an average of severa sampe spectra taken in the corresponding area of the top map. The zoomed insets show window regions (I IV) and gaseous absorption bands (V VII).

8 226 DYUDINA ET AL. FIG. 6. First four PCs for the three regions: GRS (dashed ine), Hot Spot (soid ine), and White Ova (dotted ine). The gases absorbing at different waveengths are indicated on the PC 2 pot. Correated ampitudes of the same sign mean correated deviation from the mean spectrum. Vaues of the opposite sign mean anticorreation. Neary zero vaue often means poor signa-to-noise ratio in the data image (see Figs. 1, 2, and 3). If the signa to noise is good, zero vaue means no correation. In the GRS region the refectance in vioet (0.41 µm) is anticorreated with the refectance in other waveengths ( µm), unike in the Hot Spot and White Ova regions where refectances in a waveengths are correated. This difference in PC 1 demonstrates the coor difference between the GRS and other (Hot Spot and White Ova) regions. In the GRS a vioet absorber is present where the coud is opticay thick and high (e.g., inside the GRS). In the Hot Spot and White Ova regions no vioet absorber is associated with the coud features. PC 2 (Fig. 6) shows a correation between 5-µm therma emission and brightness in absorption bands and an anticorreation between 5-µm therma emission and brightness in atmospheric windows. The PC 2 map is shown in Fig. 8. A positive coefficient A p 2 in front of PC 2 can be interpreted as a ow-atitude (dark in absorption bands) coud (bright in atmospheric windows) bocking therma emission. The upper tropospheric haze (West et a. 1986) has itte effect in the atmospheric windows because it is opticay thin, but it has a arge effect in the gaseous absorption bands because it scatters ight that woud otherwise be absorbed. Therefore PC 2 describes an anticorreation between opacity in the upper tropospheric haze and that of the ow coud, since the brightness in absorption bands is anticorreated with brightness in atmospheric windows. To bock 5-µm emission, the ow couds shoud be opticay thick in these waveengths and therefore have reativey arge coud partices (on the order of few microns or arger). We do not interpret higher order PCs. Even though they show important correations in the data, the corresponding A p i are sma and therefore the ampitudes of these variations are sma. Mathematica orthogonaity of PCs does not impy that corresponding coud properties are independent. Therefore it is hard to interpret the higher order PCs independenty from the first ones. Another reason not to interpret the higher order PCs is that detection of them is not so robust as for the first PCs (see Fig. 6 and Sections 4.2, 5.1, and 5.2). Maps for the first three PCs for the GRS are combined into a coor map shown in Fig. 5a. Since it expains 91% of the variance, this coor map is a convenient way of ooking at the data at a 26 waveengths. Instead of representing particuar waveengths, each coor shows the spatia distribution of the correated ampitude deviation in 26 waveengths. It aows one to view, as different coors, spectray different areas from a 26 maps. Areas shown by different coors in the map (Fig. 5a) have substantiay different spectra (Fig. 5b). Simiary coored areas have simiar spectra. Descriptions of the particuar areas, the corresponding spectra, and their interpretation are given beow. Area a (red in Fig. 5) represents the interior of the GRS and is brighter than the average in refected ight (both atmospheric windows and absorption bands) and is darker than the average in 5-µm emission. It is usuay interpreted as a thick, high, refecting coud containing arge partices and bocking 5-µm emission from beow. On top of this coud an opticay thick haze provides refection in absorption bands. Area b (dark bue in Fig. 5) is dark in atmospheric windows (I IV) and bright at 5 µm. That suggests that the main coud is opticay thin. Surprisingy enough, area b is bright reative to area c in deep absorption bands (V VII). Deep absorption bands dispay high-atitude couds. That supports the idea that above the opticay thin couds in the troposphere (area b) there is a stratospheric and upper tropospheric haze, and it is opticay thicker than the haze at area c. Area c (green in Fig. 5) shows an opticay thick coud (it is amost as bright in atmospheric windows as the GRS, and it bocks 5-µm emission). The coud is ocated deep reative to the other areas (it is dark in absorption bands). Area d (ight bue in Fig. 5) indicates two sma-scae bright couds to the northwest of the GRS. Aso, a simiary coored area can be observed at the east edge of the GRS. What makes area d specia? As can be ceary seen in Fig. 1, area d is the brightest spot in the µm image. Figure 5b shows the same thing: At µm, area d is brighter (higher I/F) than any other area.

9 JOVIAN CLOUD STRUCTURE FROM NIMS AND SSI IMAGES 227 FIG. 7. The maps of A p 1 (PC 1) for the GRS (upper), hot spot (ower eft), and white ova (ower right). Coefficients A p i show the amount of deviation from the mean spectrum associated with each PC i. One degree of atitude or ongitude (panetocentric coordinates) is approximatey 1200 km. The scae bar at the right of each image shows the vaues mapped. For exampe, PC 1 has high positive vaues inside the GRS (ight on the map). It means that the area is bright in the images taken in refected sunight and is dark in µm images. In most of the other waveengths area d is not very different from the average (see ight bue ine d in insets II VII). This unusua spectrum cannot be expained by the two parameters (coud opacity and eevation) that we were using above. We can think of five different mechanisms that can expain the unusua spectrum of area d. One expanation is that area d is the brightest in µm because area d is the highest coud. In other areas (for exampe at the center of the GRS) couds are ower and therefore shadowed by the gas absorption above. If that is true, curve d must be the brightest in a gaseous absorption bands (see insets V VII in Fig. 5). However curve d is not the brightest and therefore this expanation seems unikey. The second expanation is that µm absorption is due to some gas other than the ones absorbing in other waveengths. Then the unusuay ow mixing ratio of this gas above the couds in area d can make it bright. However, most of the absorption at µm is ikey to be due to CH 4 gas (see Roos- Serote et a. 1998). Therefore this expanation aso seems unikey. The third expanation is that the unusua brightness in area d can be due to the therma emission instead of refected sunight

10 228 DYUDINA ET AL. FIG. 8. The maps of A p 2 (PC 2) for the three regions. (see Roos-Serote et a. 1998). The probem is that area d is not bright at 4.8, 4.9, or 5.2 µm, which are the therma emission waveengths. The fourth expanation invoves particuate absorption. Assume that the coud partices in a other areas except area d have a µm absorber, but area d does not. Then area d wi be a bright spot in the µm image. Athough this expanation can be true, the absorber has not been identified. The ast expanation is that the partices in the coud are arge. Assuming Mie scattering (see Goody and Yung 1989 or Hansen and Travis 1974), a 5-µm partice woud be about 10 times more efficient in scattering at this waveength than a 1-µm partice. The coud in area d with 5-µm partices surrounded by couds with 1-µm partices woud stand out more at the onger waveength. This size range is consistent with other studies (see Rossow 1978, West et a. 1986). The arge-partice hypothesis is easy to expain dynamicay. The precipitation time to fa 1 scae height is years for 1-µm partices and is weeks for 5-µm partices (see Rossow 1978). Therefore it is ikey that a high popuation of arge partices woud not survive in the sow-mixing regions, but they woud survive in the fast-mixing regions the convective updrafts. Other data (Beton et a. 1996, Banfied et a. 1998) suggest that area d is a convective region PCA for the Different Regions The GRS is an unusua region on Jupiter. PCA reveas properties of the whoe region studied but not necessariy properties

11 JOVIAN CLOUD STRUCTURE FROM NIMS AND SSI IMAGES 229 of the parts of this region. To see if the principa components represent goba properties on Jupiter we performed PCA on different areas. First, we used parts of the GRS image. Aso, we studied the Hot Spot and White Ova data sets (see comparison in Section 4.1). As a genera rue, in the GRS, PC 1 remains the same within 20 30% uncertainty if the anayzed area had any contrast in a waveengths and incuded the 5-µm emission area. An exception is the anticorreation of vioet refectance with refectance in other waveengths (see Fig. 6 for the GRS where PC 1 is negative at λ = 0.41 µm). This anticorreation shows up ony at the GRS and dark coar around it; it does not show up either in other parts of the GRS region or in other (Hot Spot and White Ova) regions. PC 2 aso remained simiar (30 40% uncertainty) with the exception of the vioet waveength. This suggests a oca distribution of the chromophore over the GRS. Higher order principa components do not show much resembance and therefore do not represent homogeneousy distributed properties that can be found in every part of the studied regions. That was one of the reasons to consider ony PC 1 and PC 2 for the interpretation Reconstruction of the NIMS Images Using SSI Maps The high correation between the NIMS and SSI data suggests that SSI might serve as a proxy for a the NIMS data; in other words we may ask, what fraction of the variance in SSI NIMS data can be reconstructed using ony SSI images and PCs cacuated for 26 waveengths? This reconstruction is important because the SSI images have better resoution. If correations at the sma scae are simiar to the arge-scae correations, our reconstruction does approximate NIMS images with high resoution. Unfortunatey it is not possibe to check without having 30 km/pixe (SSI) resoution images at the NIMS waveengths. Before the reconstruction, we perform a separate PCA on the SSI data set and get four principa components in four SSI waveengths PCi SSI, where i = 1, 2, 3, 4 are the order of SSIony principa components. Then we compare PCi SSI with the fragments of PC i taken in SSI waveengths (see Fig. 9). The first two PCs show simiar correations but the third and fourth ook different. This suggests that probaby ony the first two PCs wi be usefu for the reconstruction. After our attempt to use three or four PCs instead of ony two, the accuracy of the reconstruction became substantiay worse. Accordingy, the foowing discussion wi concern the reconstruction by ony two PCs, such that q = 2. To reconstruct images in different waveengths we use the same idea as for the PCA reconstruction by first q principa components PC i u i (see Section 3.1): δx p δ X p = q i=1 Ā p i ui, where = 1, 2,...,26. Here δ denotes deviation from the mean brightness. Instead of using the ampitude coefficients A p i from the PC maps we use the coefficients Ā p i derived from SSI images as foows. For FIG. 9. Comparison of the PC SSI i (soid ine) with the fragments of PC i at SSI waveengths (dashed ine). The ampitude of correation (potted on the ordinate) for the fragments of PC i was normaized such that the fragments have unit absoute vaue in four SSI waveengths: (ui )2 = 1 where SSI. every pixe p in the four SSI images we found the best-fit coefficients Ā p 1 and Āp 2 in front of the fragments of PC 1 and PC 2 by minimizing the east square error, =1,2,4,6 ( δx p ( Ā p 1 u1 + Ā p )) 2, 2 u2 where = 1, 2, 4, 6, which are the waveength indices corresponding to the four SSI waveengths. The resuts of the reconstruction for a NIMS SSI waveengths and the corresponding data images can be seen in Fig. 10. The reconstructed images (eft images in the pair) and the data images (right images in the pair) are scaed by the brightness range for the best contrast. That aows one to see the simiarity in the geometric patterns, but not the reconstructed ampitude. The geometric patterns of the NIMS images are reconstructed we even for the 5-µm images. To quantitativey estimate the reconstruction quaity in terms of ampitude, we subtracted our reconstruction from the data, obtaining residua images R p = δx p (Ā p 1 u1 + Ā p 2 u2 ). Then for every waveength we cacuated the variance in the residua images as a fraction of the data variance. The rest of the variance V is expained by the reconstruction. V = 1 p ( R p )2 p (δx p )2. The vaues of the fractiona expained variance V for different waveengths are shown in Fig. 10. This reconstruction using the first two PCs and 4 out of the 26 images expains V = 62% (V is a V averaged over waveengths) of the tota variance in the data set (reca that the first two PCs expain 86% of the variance when the ampitudes are computed from the 26 waveengths).

12 230 DYUDINA ET AL. FIG. 10. Images of the GRS in SSI and NIMS waveengths reconstructed using PC 1,PC 2, and four SSI images (images at the eft) compared to the data (images at the right). The corresponding waveengths and percentages of the expained variance V are shown to the right of the two images.

13 JOVIAN CLOUD STRUCTURE FROM NIMS AND SSI IMAGES ERROR ANALYSIS 5.1. Spatia Resoution Effects The data set for the PCA shoud be homogeneous or for our case images in a waveengths shoud have the same spatia resoution. However, the SSI resoution is roughy 10 times better than that of NIMS. To get the same resoution for the images in a waveength we tried two methods: 1. interpoating the NIMS images at the SSI geometrica points, i.e., getting high-resoution NIMS images to put together with SSI and 2. averaging SSI pixes in a area corresponding to the NIMS pixe to get ow-resoution images for SSI waveengths. We compared the PCA resuts for both methods for the GRS and aso tried the case when the resoution was 10 times ess than that of NIMS to see the spatia-resoution effect. The first few principa components were amost exacty the same for cases 1 and 2 above. Namey, the difference of the principa components is ess than 0.1%, 0.15%, 0.5%, and 2% for first, second, third, and fourth PCs respectivey (the difference is evauated at the waveength where it is greatest and is normaized by the peakto-trough ampitude of the PC). For a very coarse resoution (10 times NIMS) first principa components are sti very simiar to the ones for SSI resoution (with differences of ess than 2%, 2%, 15%, 20%). The simiarity in principa components for different spatia resoutions suggests that the PCs dispay arge-scae features rather than sma-scae coud variations. FIG. 11. Signa-to-noise ratio for the GRS at different waveengths used for the noise-based normaization. The detector noise is assumed to be 5 DN. normaized by the observationa noise (Fig. 11). As a resut, the ampitudes of the data images differ by an order of magnitude at different waveengths. The resuting PCs are simiar to the ones obtained in PCA with the standard normaization (see the case of the GRS in Fig. 12) Observationa Noise Effect The brightnesses in different waveengths are subject to observationa noise (therma, instrumenta, cosmic-ray-induced, etc.). It is different for different waveengths. In SSI images it is roughy the digitization eve (the noise is on the order of 1 data number (DN), whie the signa approaches 255 DN). For NIMS the gain for the detectors is the same for a waveengths (see Carson et a. 1992). The detector noise is a few percent of 256 DN, which is a maximum signa eve. The actua signa eve changes from waveength to waveength giving different signato-noise ratios (see Fig. 11). To study the sensitivity of PCA to observationa noise, we tested the response to random noise added to the GRS data. Emuation of reaistic detector noise (which has a standard deviation of 5 DN in each detector) gave an agreement of PC 1 within 3% at λ<4µmand within 16% at 4 5 µm; PC 2 gave agreement within 3% everywhere; both PC 3 and PC 4 gave agreement within 25%. PC 5 and higher order PCs varied substantiay at different reaizations of random noise. Therefore ony the first four PCs are robust in representing the atmospheric properties at the GRS Noise-Based Normaization To check the stabiity of our resuts, instead of normaizing each waveength by its standard deviation (see Section 3.1), we FIG. 12. First four principa components for the GRS cacuated using standard normaization (soid ines) and noise-based normaization (dashed ines).

14 232 DYUDINA ET AL. TABLE II Percentages of Variance Associated with the Principa Components in the Case of Standard and Noise-Based Normaization PC 1 (%) PC 2 (%) PC 3 (%) GRS Standard normaization Noise-based normaization Hot Spot Standard normaization Noise-based normaization White Ova Standard normaization Noise-based normaization Percentages of the expained variance for the noise-based normaization are simiar to ones for the standard normaization. The comparison is given in Tabe II Waveength Uncertainty The waveength caibration of NIMS images (see Carson et a. 1992) changes during the mission. The waveength shift during orbit is estimated to be on the order of 50 Å (0.005 µm), which is tens of percents of detector bandwidth. The PCA resuts do not incude waveength caibration and do not depend on the exact waveength vaue. The waveength shift aso is too sma to be important when we have to decide if the waveength beongs to the absorption band. 6. DISCUSSION The PC 1 map (Fig. 7) shows increased optica thickness and increased eevation of the coud inside the GRS and White Ova (see Section 4.1). This resut is consistent with other studies performed on the parts of the same data set. It agrees with the coud structure derived for the GRS by Weir et a. (1997) using a point-by-point fit to the NIMS maps in four near-infrared waveengths. In their resuts the midde of the GRS is eevated and coudy above 0.6 bars, which is about the NH 3 condensation eve assuming soar NH 3 mixing ratio. Banfied et a. s (1998) concusions are based on fits to the SSI images in three waveengths with varying observationa geometry. These resuts show the same increases in optica depth and coud eevation over the GRS and decrease in the coar around it. The sma couds to the northwest of the GRS (our area d in Fig. 5) were interpreted by Banfied et a. (1998) to be extremey opticay thick and high (optica depth > 20 at 400 mbar). Our resuts agree with that and in addition suggest the presence of arge partices (see Section 4.1), impying unusuay strong precipitation. Comparison with Banfied et a. s (1998) mode is especiay important as we used the same data but combined them with NIMS images. According to West et a. (1986), an opticay thick coud near the NH 3 condensation eve shoud contain arge NH 3 -ice partices (3 100 µm) snowing down to the equiibrium condensation eve where they subimate. NH 3 gas is highy depeted in the coud by precipitation. To support optica thickness of the coud, there shoud be a source of fresh NH 3 at the coud eve. There are two mechanisms to bring NH 3 to the coud from the ower eves: a arge-scae updraft and turbuence. It is ikey that both mechanisms work together. Both the updraft and increased turbuence woud eevate the upper boundary of the coud by bringing NH 3 to higher atitudes. We interpret PC 1 as a measure of coud optica thickness correated with the coud eevation (see Section 4.1) Therefore, the positive vaues on the PC 1 map can be interpreted as an updraft and/or an increase in turbuence at east as high as the NH 3 condensation eve. The PC 2 map in Fig. 8 shows an anticorreation between the high tropospheric haze and the ow 5-µm absorbing coud. This anticorreation dominates where the PC 1 ampitude is sma and the PC 2 ampitude is arge. It cannot be expained by the updraft or downdraft continuing through troposphere to stratosphere. According to West et a. (1986) the haze is ikey to be composed of 1-µm-size partices. The ifetime of these partices against precipitation is of the order of years (Rossow 1978), and a high optica depth can be supported by rather gente mixing in the atmosphere. 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